Question: Rewrite as a simplified fraction. ${0.57\overline{3} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 573.3333...\\ 100x &= 57.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 516}$ ${x = \dfrac{516}{900}} $ ${x = \dfrac{43}{75}} $